That's the opposite of independence. It means that the same party needs to do both CPU and GPU to validate their block. So end users can't mine because they don't have GPUs. And there's no way to adjust difficulty separately since you don't have separate blocks to count.
No it wouldn't. It would simply be a public double signing.
Two algorithms lets call them C & G (for obvious reasons).
A pool of G miners find a hash below their target and sign the block and publish it to all other nodes in network. The block is now half signed.
A pool of C miners then take the half signed block and look for a hash that meets their independent target. The block is now fully signed.
Simply adjust the rules for a valid block then for those half signing they can only generate a reward half the size + half transaction fees. The second half does the same. So the G miner (or pool) who half signs the block gets 25BTC + 1/2 transaction fees, the C miners would complete the half signed block get the other 25 BTC + 1/2 the transaction fees.
A block isn't considered confirmed until both halves of the hash pair are complete and published. If you want block signing to take 10 minutes of average adjust the difficulty for each half so that average solution takes 5 minutes for half signed block.
While I doubt any dual algorithm solution is needed it makes more sense to have both keys required otherwise bitcoin becomes vulnerable to the weaker of either algorithm (which is worse than having single algorithm).
, but I haven't worked through all the details yet, so I'm not confident enough to use that label yet. Think carefully about the coinbase transactions, and how those are included (or not) in the half signatures. I'm pretty sure that this system ends up being no better than just the second half system, but it could be modified to be as good as whichever system was slower at the moment.